Popular numerical discretizations of the forward problem for the incompressible Euler equations on periodic domains are spectral methods [1]}, [2]}, [3]}, [4]}. In this section, we will review the spectral (hyper-)viscosity methods, originally proposed by Tadmor [5]} in the context of scalar conservation laws, and further investigated in [6]}, [7]} in the context of the incompressible Euler equations.
